Bounds on the dimension of certain codes and subcodes

Alexander Vardy*, Jakov Snyders, Yair Be'ery

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review


Summary form only given, as follows. Let C be an (n, k) linear block code over GF(q), generated by a matrix G. A nonnegative integer λ is said to be the contraction index of C if a maximal set of pairwise linearly independent columns of G has k + λ elements. In recent works of Conway and Sloane, Be'ery and Snyders and Forney, it was shown that the complexity of soft decision decoding of block and lattice codes can be considerably reduced by means of partitioning the code into cosets with respect to a subcode of large dimension and small contraction index. The present authors derive several upper and lower bounds on the dimension of a subcode with a prescribed contraction index. They also present an upper bound on the dimension of any (n,k) code over GF(q), with minimum Hamming distance d and contraction index λ. For certain values of n and d, the latter bound is shown to be tight for all q and λ. This substantially generalizes the results obtained previously for λ = 1 in the context of majority logic decoding.

Original languageEnglish
Number of pages1
StatePublished - 1990
Event1990 IEEE International Symposium on Information Theory - San Diego, CA, USA
Duration: 14 Jan 199019 Jan 1990


Conference1990 IEEE International Symposium on Information Theory
CitySan Diego, CA, USA


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